Question

When should we use other than classical interpretations of probability?

Answer 1

CLASSICAL INTERPRETATIONS OF PROBABILITY::-

Since likelihood analytics has been axiomatized, Kolmogorov's axiomatization being the standard one, and the one we quickly considered in this course, one may basically say that likelihood is whatever fulfills the sayings of likelihood, much similarly in which, say, Euclidean things are whatever fulfills Hilbert's axiomatization of geometry. Numerous amounts, for example, standardized length, fulfill the maxims of likelihood. Be that as it may, such amounts don't give an elucidation of likelihood in the feeling of an examination of the idea of likelihood, which, apparently, is the thing that one has as a main priority when one asks what likelihood is. Consequently, accepting that the inquiry isn't not well presented, one may want to participate in some scientific/philosophical contemplations.

main interpretations of probability are best divided into into two groups:

1. Epistemological interpretations, according to which probability is primarily related to human knowledge or belief.
2. Objective interpretations, according to which probability is about a feature of reality independent of human knowledge or belief.

The Classical interpretation (Bernoulli, Laplace)::-

1. Determinism obtains in the natural world.  Hence, probability is epistemic.
2. To determine the probability of, say, getting a 2 when tossing a fair die, we constructed the ratio between favorable cases and possible cases.  Probability is such ratio.
3. Ratios between favorable and possible cases can be easily shown to obey the axioms of probability calculus.

The probability of a single event (e.g., the murder of Caesar) cannot be determined by constructing a ratio, as there seem to be no relevant equiprobable cases